The capacity gain proportional to the number of transmit or rceive antenna promised by MIMO, has attracted many interests to implement MIMO on existing terrestial and satellite system. A complementary to those existing systems is known as HAPS,and is situated in the stratosphere around 17-22 km. One of the interesting applications of HAPS is broadband transmission to high speed trains. The requirements of simultaneously transmitting hugh data rate in the order of tens if Mbps t high speed trains has brought the idea of implementing multiuser MISO on HAPS. The donwlink channel where HAPS is equipped with more than one antenna transmitting to more than one single-antenna trains simultaneously, is know as the Guassian MISO broacast channel. The capacity region for this channel is achieved by DPC, but is diffcult to implement in practical systems. In this paper, a suboptimal lower complexity schene such as ZF beamforming is utilized as the precoding strategy. A simulation is conducted to calculate the sum rate capacity for different SNRs. The channel is i.i.d. Rayleigh and Ricean distributed and is assumed to be known perfectly both by the transmitter and receiver. The receiver is assumed to have compensated for the doppler perfectly. The result is compared to the theoretically optimal DPC strategy and also to the DOA tecnique proposed by one of the HAPS project in Europe (CAPANINA).